This volume contains the proceedings of the BIRS Workshop ""Topics in Multiple Time Scale Dynamics"", held from November 27- December 2, 2022, at the Banff International Research Station, Banff, Alberta, Canada. The area of multiple-scale dynamics is rapidly evolving, marked by significant theoretical breakthroughs and practical applications. The workshop facilitated a convergence of experts from various sub-disciplines, encompassing topics like blow-up techniques for ordinary differential equations (ODEs), singular perturbation theory for stochastic differential equations (SDE), homogenization and averaging, slow-fast maps, numerical approaches, and network dynamics, including their applications in neuroscience and climate science. This volume provides a wide-ranging perspective on the current challenging subjects being explored in the field, including themes such as novel approaches to blowing-up and canard theory in unique contexts, complex multi-scale challenges in PDEs, and the role of stochasticity in multiple-scale systems.
Maximilian Engel, Free University of Berlin, Germany, and University of Amsterdam, The Netherlands, Hildeberto Jardon-Kojakhmetov, Bernoulli Institute, University of Groningen, The Netherlands, and Cinzia Soresina, University of Graz, Austria
Riccardo Bonetto and Hildeberto Jardon-Kojakhmetov, A topological perspective on singular canards for critical sets with transverse intersections Maximilian Engel and Georg A. Gottwald, Canards in modified equations for Euler discretizations Maximilian Engel and Guillermo Olicon-Mendez, Noise-induced instabilities in a stochastic Brusselator S. Jelbart and C. Kuehn, A formal geometric blow-up method for pattern forming systems Christian Kuehn, Pascal Lehner, and Jan-Eric Sulzbach, Infinite dimensional slow manifolds for a linear fast-reaction system Adam H. Monahan, Spectral and bispectral densities of squared stationary Guassian processes Elle Musoke, Bernd Krauskopf, and Hinke M. Osinga, A heteroclinic surface between two saddle slow manifolds organizing sectors of rotation of mixed-mode oscillations Nikola Popovic and Zhouqian Miao, The effect of a cut-off on a model of invasion with dispersive variability Cinzia Soresina, Bao Quoc Tang, and Bao-Ngoc Tran, Fast-reaction limits for predator-prey reaction-diffusion systems: improved convergence Xiaoxuan Wu and Tasso J. Kaper, A new class of multi-scale reaction-diffusion systems with closed-form, low-dimensional, invariant manifolds
